# MPhys Physics with Astrophysics

Year of entry: 2024

## Course unit details:Random Processes in Physics

Unit code PHYS10471 10 Level 1 Semester 1 Department of Physics & Astronomy No

### Overview

Random Processes in Physics

### Aims

To introduce and develop the mathematical skills and knowledge needed to understand and use probability theory in physics.

### Learning outcomes

On completion of the course, students will be able to:

1. Be cognizant of and be able use appropriately, the fundamentals of probability theory.
2. Set up and solve models of physical processes involving randomness.
3. Be aware of and be able to critically apply, some of the important probability distributions that are used by physicists.

### Syllabus

1.  Elements of probability

• Introduction:  What is probability?
• How to calculate probabilities:  permutations and combinations
• Conditional probability

2.  Probability distributions

• Discrete random variables; expectation value and variance
• Example:  the geometric distribution
• Continuous random variables; the probability density function
• Examples:  the uniform distribution; the normal (or Gaussian) distribution

3. Exponential Probability Distribution

• Probability of collisions in a gas; mean free path
• Generalisation: “hazard rate” and survival probability

4. Poisson Probability Distribution

• Probability of occurrence of n random events
• Properties of the Poisson distribution
• Gaussian limit of the Poisson distribution

5. Binomial Probability Distribution

• Binomial distribution for n trials
• Irreversible expansion of a gas
• Poisson and Gaussian limits of the binomial distribution
• Random walks and diffusion

### Assessment methods

Method Weight
Written exam 100%

### Feedback methods

Feedback will be provided through self assessed problems, and on-line assessment of weekly examples sheets. General feedback will also be given during the weekly Q&A session.

A suitable introduction to probability can be found in:

Chapters 39 and 40 of Mathematical Techniques, 3rd edition, Jordan, D. & Smith, P.

Chapters 20 & 21 of Mathematics for Engineers and Scientists, Weltner, K., Gorsjean, J., Schuster, P. & Weber, W.

Chapter 3 of Statistics, Barlow, R.J.

### Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 22
Seminars 6
Independent study hours
Independent study 70.5

### Teaching staff

Staff member Role
Michael Keith Unit coordinator
Benjamin Stappers Unit coordinator